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lfunc_lfunctions • Show schema
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{'Lhash': '483478926087699034486912790080', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.3083759502061423, -1.1349680052416342], 'a4': [0, 0], 'a5': [0, -2.23606797749979], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0.42369525415565124, 2.969929684623186], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.852174775958158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.3083759502061423, 1.1349680052416342]]], [5, [[1.0, 0], [0, 2.23606797749979]]], [31, [[1.0, 0], [5.5677643628300215, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.929', 'coefficient_field': 'CDF', 'conductor': 1860, 'conductor_radical': 930, 'conjugate': '1603695422969891151290168375965', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.3083759502061423, 1.1349680052416342]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [0, 0], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], 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'5.12349849816148679930532690395698', '6.03075290760343983900957271120374', '6.61807993186470968661769997076999', '7.28128950257846491085654792632398', '8.642405856250692428120389526277048', '9.052331009197492355467670681440595'], 'prelabel': '2-1860-465.464-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8538519400669973, 'root_angle': -0.1362765675745279, 'root_number': '0.655274083347870135185206505857046008288272348753721041 - 0.755391207052748624464104660329433187041996864704912538*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13627656757452794', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38139762328882492004613827073', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18069929235592057839426195137', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43896908724563219362423212558', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.852174775958158, 'bad_primes': [2, 3, 5, 31], 'central_character': '465.464', 'conductor': 1860, 'conductor_radical': 930, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/2/i/a/929/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-1860-465.464-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1860-465.464-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8538519400669973, 'root_angle': -0.1362765675745279, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38139762328882492004613827073', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '483478926087699034486912790080', 'Lhash_array': ['483478926087699034486912790080'], 'factors': ['2-1860-465.464-c1-0-12'], 'label': '2-1860-465.464-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/2/i/a/929/3'}